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Re: - FFT and Mathematica
On Sat, 8 Apr 1995 David E. Burmaster: > Dear MathGroupers > > Can someone pls recommend a book or an article that discusses how to use > FFT in Mathematica?? ..... hopefully something with lots of examples, > including convolutions done using FFTs.... > > Thank you for your help...... > > Dave > David E. Burmaster Dear Dave, I recommend you the book: Richard E. Crandall, "Projects in Scientific Computation", Springer-Verlag, New York, 1994. This book is about computation in many fields, but there is a paragraph (4th) about FFT (pages 151 - 195). For this book is a floppy disk included with the examples in two formats: Mathematica Notebook or C source code. It is a short list of this paragraph: 4. The FFT forest. The ubiquitous FFT and its relatives. 4.1 Discrete Fourier transform 4.1.1 Fundamental DFT manipulations 4.1.2 Algebraic aspects of the DFT 4.1.3 DFT test signals (+ "DFTgraphs.ma" mma notebook file) 4.1.4 DFT software (+ "fft.c" C source code file) 4.2 FFT algorithms 4.2.1 Recursive FFTs (+ "DanielsonLanchos.ma mma notebook file) 4.2.2 FFT indexing and butterflies 4.2.3 Complex FFTs, N a power of 2 (+ "FFTs.ma" mma notebook file) 4.2.4 Real-signal FFTs (+ "fft_real.c C source code file) 4.2.5 FFTs for other radices 4.2.6 FFTs in higher dimensions 4.2.7 Applications of the FFT 4.3 Real-valued transforms 4.3.1 Hartley transform (+ "RecursiveFHT.ma" mma notebook file) 4.3.2 Discrete cosine transform 4.3.3 Walsh-Hadamard transform (+ "walsh.c" C source code file) 4.3.4 Square-wave transform (+ "FSWT.ma" mma notebook file) 4.4 Number-theoretic transforms 4.4.1 Exploring Number-theoretic transforms If you want I can send to you these source text files. It is a fragment of "prohibitions" from "readme" file included with the book: "[...] This electronic component package is protected by federal copyright law and international treaty. The copyright holder retains title to and ownership of the package. US copyright law prohibits you from making any copy of the diskette for any reason, without the written permission of Springer-Verlag, except that you may download and copy the "readme" and source text files for your own research, teaching, and personal communications use. [...] The printed book with which this electronic component is packaged may not be translated or copied in whole or in part without the written permission of Springer-Verlag except for brief excerpts in connection with reviews or scholarly analysis. [...]" The other source may be a Signal Processing Packages and Notebooks, it is "a hierarchical set of packages to perform basic analyses of signals (functions) and systems (operators). The packages are based on transform theory and implement many concepts from linear transform theory. They support (bilateral) z- and Laplace transforms, as well as continous-time, discrete-time, and discrete Fourier transforms, all in arbitrary dimension. [...]" This package is available for DOS, Unix and Macintosh systems by ftp from MathSource (mathsource.wri.com), item No. 0202-240, or from gauss.eedsp.gatech.edu, Mathematica directory. Hope this help, Grzegorz.